FM FM Interest Rate Theory

Question 1

What is the relationship between the nominal rate compounded monthly (i^(12)) and the equivalent effective annual rate i?

Accepted Answer

(1 + i) = (1 + i^(12)/12)^12

Answer

The effective annual rate i satisfies (1 + i) = (1 + i^(12)/12)^12, converting monthly compounding to an annual equivalent.

Question 2

The force of interest δ is related to the effective annual rate i by which formula?

Accepted Answer

δ = ln(1 + i)

Answer

The force of interest δ equals the natural logarithm of the accumulation factor: δ = ln(1 + i).

Question 3

An account pays a nominal interest rate of 6% compounded semiannually. What is the effective annual rate?

Accepted Answer

6.09%

Answer

EAR = (1 + 0.06/2)^2 − 1 = (1.03)^2 − 1 = 0.0609 = 6.09%.

Question 4

Under simple interest, the accumulation function a(t) is:

Accepted Answer

a(t) = 1 + it

Answer

Simple interest grows linearly, so the accumulation function is a(t) = 1 + it.

Question 5

The discount rate d and the interest rate i satisfy which relationship?

Accepted Answer

d = i / (1 + i)

Answer

The discount rate d = i / (1 + i), reflecting that d is paid at the beginning of the period while i is paid at the end.

FM - Certifications in Financial Mathematics Practice Test